09/03/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building
Anatoli Merzon, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Mexico
About the scattering of plane waves by wedges
We consider a nonstationary scattering of plane waves by a
wedge. It is assumed that the incident wave does not depend on the
coordinate parallel to the the edge of the wedge, so the problem is
planar. Also we assume that, beginning with a certain time instant
depending on a spatial position of the point, the incident wave is
periodic in time with the frequency \(\omega\) in each point of the
space. Let the profile of the wave be such that the incident wave
has the front ahead of which it is zero. Therefore the incident
wave establishes a harmonic vibration at any point of the
complement of the wedge with the frequency \(\omega\). The main
goal is to prove that the amplitude of the solution to the
corresponding mixed problem for the D'Alembert equation with
initial data determined by the incident wave, tends to the
solutions of the classical stationary diffraction problem. Thus,
these classical solutions can be represented as the limiting
amplitudes of the solutions to the non-stationary problem, i.e. the
Limiting Amplitude Principle holds. It is proved for the Dirichlet
and Neumann boundary conditions and for Dirichlet-Neumann boundary
conditions only for the right angle.